Subband coding is one of the most popular signal coding techniques known to date. The conventional subband coding paradigm consists of first splitting the input signal into frequency bands, and then coding the subbands. Individual subband coding systems differ typically in the choice of subband configuration, quantizers, entropy coders and bit allocation strategy. Much of the performance gain associated with subband coding may be attributed in general to the removal of linear dependencies among subband signals by the filter bank. However, additional gain may be attained by recognizing that the subband signals are generally not statistically independent. Therefore, quantizers and entropy coders that are optimized to the statistics of all subband signals can lead to a significant improvement in rate-distortion performance.
Previously, a generalized subband decomposition framework that provides a way of determining necessary conditions for the optimality of entropy constrained subband quantizers given an arbitrary set of filters and an arbitrary decomposition structure was proposed in F. Kossentini, W. Chung and M. Smith, "Subband Image Coding With Intra- And Inter-Band Subband Quantization, " in Asilomar Conf. on Signals, Systems and Computers, (Pacific Grove, Calif., November 1993). Subband quantizers and entropy coders were designed jointly to minimize the average distortion subject to a constraint on the output rate of the system. The subband coder of the present invention presents a joint optimization entropy constrained subband quantization design algorithm with emphasis on complexity reduction that leads to improved complexity-performance tradeoffs. The subband coder of the present invention exploits both linear and non-linear dependencies that may exist within and across the subbands. Both inter- and intra-band dependencies are simultaneously exploited via jointly optimizing the subband encoders, decoders, and entropy coders in an entropy constrained optimization framework involving rate, distortion and complexity.